The U-2 program was the game changer. It revealed that the USSR was testing missiles but was not able yet to deploy them.
The political problem for the administration that attached to the Sputnick "shock" rested with the fact that Eisenhower, and only a handful of other key officials, knew about the top-secret U-2 program that was capable of providing aerial surveillance of the USSR's missile installations and other military capability.
Numerous U-2 flights since 1956 has shown Eisenhower and his small team that the Soviet Union was by no means ahead of the United States in any major category. Given this knowledge, the president fought back attempts to remedy our vulnerabilities with crash military programs—and expenditure of more money—as the primary way to salve the nation's bruised ego.
As Eisenhower thought about how to manage the valuable U-2 program, he was convinced that it would be a more effective means of intelligence gathering if it remained secret. Nevertheless, the information could have removed much of the political heat the president faced; even Secretary of State John Foster Dulles encouraged him to use the U-2 information as a way to reassure the public. But as Barry Goldwater later observed, "Ike took the heat, grinned, and kept his mouth shut."
-Susan Eisenhower, How Ike Led: The Principles Behind Eisenhower's Biggest Decisions